Related papers: Floquet defect solitons
We obtain sharp criteria for transverse stability and instability of line solitons in the discrete nonlinear Schr\"{o}dinger equations on one- and two-dimensional lattices near the anti-continuum limit. On a two-dimensional lattice, the…
The concept of spectrum for a class of non-linear wave equations is studied. Instead of looking for stability, the key to the spectral structure is found in the instability phenomena (bifurcations). This aspect is best seen in the…
We predict that a photonic crystal fiber whose strands are filled with a defocusing nonlinear medium can support stable bright and also vortex solitons if the strength of the defocusing nonlinearity grows toward the periphery of the fiber.…
In this study, we investigate the existence and stability of in-phase and out-of-phase dissipative solitons in a dual-waveguide lattice with linear localized gain and nonlinear losses under both focusing and defocusing nonlinearities.…
We analyze the properties and stability of two-color discrete localized modes in arrays of channel waveguides where tunable quadratic nonlinearity is introduced as a nonlinear defect by periodic poling of a single waveguide in the array. We…
We study the effect of lifting the degeneracy of vortex modes with a PT symmetric defect, using discrete vortices in a circular array of nonlinear waveguides as an example. When the defect is introduced, the degenerate linear vortex modes…
We report on existence and properties of discrete gap solitons in zigzag arrays of alternating waveguides with positive and negative refractive indices. Zigzag quasi-one-dimensional configuration of waveguide array introduces strong…
We show that an inhomogeneous defocusing nonlinearity that grows toward the periphery in the positive and negative transverse directions at different rates can support strongly asymmetric fundamental and multipole bright solitons, which are…
We reveal and observe experimentally significant modifications undertaken by discrete solitons in waveguide lattices upon the continuous transformation of the lattice structure from one-dimensional to two-dimensional. Light evolution and…
The propagation of linear and nonlinear edge modes in bounded photonic honeycomb lattices formed by an array of rapidly varying helical waveguides is studied. These edge modes are found to exhibit strong transmission (reflection) around…
We consider a topological Floquet insulator realized as a honeycomb array of helical waveguides imprinted in weakly birefringent medium. The system accounts for four-wave mixing occurring at a series of resonances arising due to Floquet…
We study the light transmission in two-dimensional photonic crystal waveguides with embedded nonlinear defects. First, we derive the effective discrete equations with long-range interaction for describing the waveguide modes, and…
We introduce topological vector edge solitons in a Floquet insulator, consisting of two honeycomb arrays of helical waveguides with opposite directions of rotation in a focusing nonlinear optical medium. Zigzag edges of two arrays placed in…
We experimentally demonstrate the formation and stable propagation of various types of discrete temporal solitons in an optical fiber system. Pulses interacting with a time-periodic potential and defocusing nonlinearity are shown to form…
Fundamental solitons pinned to the interface between three semi-infinite one-dimensional nonlinear dynamical chains, coupled at a single site, are investigated. The light propagation in the respective system with the self-attractive on-site…
We study how the nonlinear propagation dynamics of bulk states may be used to distinguish topological phases of slowly-driven Floquet lattices. First, we show how instabilities of nonlinear Bloch waves may be used to populate Floquet bands…
We show theoretically that a photonic topological insulator can support edge solitons that are strongly self-localized and propagate unidirectionally along the lattice edge. The photonic topological insulator consists of a Floquet lattice…
We discuss the formation of self-trapped localized states near the edge of a semi-infinite array of nonlinear waveguides. We study a crossover from nonlinear surface states to discrete solitons by analyzing the families of odd and even…
We present a progress overview focused on the recent theoretical and experimental advances in the area of soliton manipulation in optical lattices. Optical lattices offer the possibility to engineer and to control the diffraction of light…
We study the coupling between backward- and forward-propagating wave modes, with the same group velocity, in a composite right/left-handed nonlinear transmission line. Using an asymptotic multiscale expansion technique, we derive a system…